Critical nucleation length for accelerating frictional slip

TL;DR

This paper introduces a new theoretical method to determine the critical nucleation length for accelerating slip in frictional interfaces, improving predictions relevant to earthquake physics and other systems.

Contribution

The authors propose an alternative linear stability analysis approach that yields a larger and more accurate critical nucleation length compared to traditional methods.

Findings

The new approach produces a larger critical nucleation length with the same scaling.

Finite-size and bimaterial interface effects are analytically derived.

Numerical simulations agree well with the theoretical predictions.

Abstract

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical and engineering systems, with particularly far-reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length $L_c$. The critical nucleation length $L_c$ is conventionally obtained from a spring-block linear stability analysis extended to interfaces separating elastically-deformable bodies using model-dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically-deformable bodies. For elastically identical half-spaces and rate-and-state friction, the two approaches are shown to yield $L_c$ that features the same scaling structure, but with substantially different numerical pre-factors, resulting in a significantly larger $L_c$ in our approach. The proposed approach is also shown to be naturally applicable to finite-size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite-Element-Method calculations for a finite-size two-dimensional elastically-deformable body in rate-and-state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted $L_c$ and its finite-size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.